$\smallint \,\,\frac{{{{\log }_e}\,\,\left( {\tan \,\,x} \right)}}{{\sin \,\,x\,\,\cos \,\,x}}\,\,dx$ is equal to

${\left[ {{{\log }_e}\,\,\left( {\tan \,\,x} \right)} \right]^2} + \,\,c\,$

${\log _e}\,\,\left( {{{\log }_e}\,\,\tan \,\,x} \right) + \,\,c$

${\log _{\rm{e}}}\,\,\tan \,\,x\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{{{\log }_e}\,\,\left( {\tan \,\,x} \right)}}{{\sin \,\,x\,\,\cos \,\,x}}\,\,dx

is equal to

View answer and explanation

Correct option: B

\,\frac{1}{2}\,\,{\left( {{{\log }_e}\,\tan \,\,x} \right)^2} + \,\,c

Option B is correct because the integral simplifies to

\frac{1}{2}\,{\left( {\log _e}\,\tan \,x} \right)^2} + \,c

after applying u-substitution twice.